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SSAT Middle Level Math : SSAT Middle Level Quantitative (Math)

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Example Questions

Example Question #173 : How To Divide Fractions

Hydraulic fracturing is a process used by gas companies to rupture and collect pockets of gas trapped within pockets of shale rock. A particular shale fracking site is $\frac{3}{4}\textup{ miles}$ in length and occupies an area of $\frac{1}{2}\textup{ miles}^2$ . How wide is this particular site?

Possible Answers:

$\frac{6}{7}\textup{ miles}$

$\frac{2}{3}\textup{ miles}$

$\frac{2}{5}\textup{ miles}$

$\frac{3}{5}\textup{ miles}$

$\frac{1}{3}\textup{ miles}$

Correct answer:

$\frac{2}{3}\textup{ miles}$

Explanation:

In order to solve this question, we need to first recall how to find the area of a rectangle.

$\text{Area}=\text{Length} \times \text{Width}$

Substitute in the given values in the equation and solve for $\text{Width}$ .

$\frac{1}{2}\ miles^2=\frac{3}{4}\ miles\times Width$

Divide both sides by $\frac{3}{4}\ miles$

$\frac{\frac{1}{2}\ miles^2}{\frac{3}{4}\ miles}=\frac{\frac{3}{4}\ miles \times Width}{\frac{3}{4}\ miles}$

Dividing by a fraction is the same as multiplying by its inverse or reciprocal.

Find the reciprocal of $\frac{3}{4}\ miles$

$\frac{3}{4}\ miles\rightarrow \frac{4}{3}\ miles$

Simplify and rewrite.

$Width=\frac{4}{3} \times \frac{1}{2}$

Multiply and solve.

$Width=\frac{4}{6}$

Reduce.

$Width=\frac{2}{3}\ miles$

The width of the fracking site is $\frac{2}{3}\ miles$

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Example Question #23 : Solve Division Word Problems With Fractions And Whole Numbers: Ccss.Math.Content.5.Nf.B.7c

How many $\frac{1}{3}\textup{ cup}$ servings are in five cups of chocolate chips?

Possible Answers:

Correct answer:

Explanation:

Because we want to know how many $\frac{1}{3}\textup{ cup}$ servings are in cups, we are dividing by $\frac{1}{3}$ .

Remember, whenever we divide by a fraction, we multiply by the reciprocal

$\frac{5}{1}\times\frac{3}{1}=\frac{15}{1}=15$

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Example Question #1 : How To Add Fractions

$1 \frac{1}{2} + 2 \frac{3}{4} =$

Possible Answers:

4.7

3.25

4.5

3.75

4.25

Correct answer:

4.25

Explanation:

I think the easiest way to do this problem is to make a common denominator. 4 is the smallest common denominator.

$2 \frac{3}{4}$ is equivalent to $\frac{11}{4}$ .

When you add $\frac{6}{4}$ and $\frac{11}{4}$ you get $\frac{17}{4}$ .

$\frac{17}{4}$ reduces to $4 \frac{1}{4}}$ and is equivalent to 4.25 .

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Example Question #224 : Grade 7

Evaluate:

-3.2+7.17

Possible Answers:

-3.97

6.85

-7.49

-10.37

3.97

Correct answer:

3.97

Explanation:

The sum of two numbers of unlike sign is the difference of their absolute values, with the sign of the "dominant" number (the positive number here) affixed:

-3.2+7.17 = +(7.17 - 3.2) = 7.17 - 3.2

Subtract vertically by aligning the decimal points, making sure you append the 3.2 with a placeholder zero:

7.12

$\underline{3.20}$

3.97

This is the correct choice.

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Example Question #2 : How To Add Fractions

Evaluate:

$6 \frac{3}{7}- 4 \frac{1}{7} + 1 \frac{6}{7}$

Possible Answers:

$12\frac{3}{7}$

$8 \frac{5}{7}$

$5 \frac{2}{7}$

$4 \frac{1}{7}$

$\frac{3}{7}$

Correct answer:

$4 \frac{1}{7}$

Explanation:

Rewrite these numbers as improper fractions.

$6 \frac{3}{7}= \frac{6 \cdot 7 + 3}{7}= \frac{45}{7}$

$4 \frac{1}{7}=\frac{4 \cdot 7+ 1}{7} = \frac{29}{7}$

$1 \frac{6}{7} = \frac{1 \cdot 7 + 6}{7} = \frac{13}{7}$

Now evaluate:

$6 \frac{3}{7}- 4 \frac{1}{7} + 1 \frac{6}{7}$

$= \frac{45}{7}- \frac{29}{7}+ \frac{13}{7}$

$= \frac{45-29+13}{7}$

$= \frac{16+13}{7}$

$= \frac{29}{7}$

$29 \div 7 = 4 \textrm{ R }1$ , so

$\frac{29}{7} = 4 \frac{1}{7}$

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Example Question #482 : Arithmetic

Add:

$\frac{1}{12}+\frac{4}{3}$

Possible Answers:

$\frac{1}{3}$

$\frac{5}{3}$

$\frac{17}{3}$

$\frac{17}{12}$

$\frac{19}{12}$

Correct answer:

$\frac{17}{12}$

Explanation:

Rewrite using the lowest comon denominator. Since LCM (12, 3) = 12 :

$\frac{1}{12}+\frac{4}{3}$

$= \frac{1}{12}+\frac{4 \times 4}{3 \times 4}$

$= \frac{1}{12}+\frac{16}{12}$

$= \frac{16+1}{12}$

$= \frac{17}{12}$

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Example Question #483 : Arithmetic

$\frac{2}{3} + \frac{1}{6}$

Possible Answers:

$\frac{1}{3}$

$\frac{1}{6}$

$\frac{5}{6}$

$\frac{3}{9}$

$\frac{1}{2}$

Correct answer:

$\frac{5}{6}$

Explanation:

When adding fractions, both denominators must be the same. A quick and easy way to do this is to multiply the numerator and the denominator of each fraction by the other fraction's denominator:

$\frac{2}{3} \times \frac{6}{6} = \frac{12}{18}$ and $\frac{1}{6} \times \frac{3}{3} = \frac{3}{18}$

The $\tfrac{2}{3}$ is multiplied by 6 on both ends because the denominator of $\tfrac{1}{6}$ is 6. Likewise, $\tfrac{1}{6}$ is multiplied by 3 on both ends because the denominator of $\tfrac{2}{3}$ is 3. The problem should now look like this:

$\frac{12}{18} + \frac{3}{18} = \frac{15}{18}$

Remember to reduce. 15 and 18 are both divisible by 3.

$\frac{15}{18} = \frac{5}{6}$

Your answer is $\frac{5}{6}$ .

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Example Question #3 : How To Add Fractions

Add the following fractions and simplify, if possible.

$\frac{3}{4}+\frac{1}{2}$

Possible Answers:

$\frac{2}{3}$

$\frac{1}{3}$

$\frac{1}{2}$

$\frac{5}{4}$

Correct answer:

$\frac{5}{4}$

Explanation:

In order to add fractions with different denominators, first find a common denominator of the fractions by finding the least common multiple. The least common multiple of these denominators is:

4*1=4 and 2 * 2 = 4 .

Because $\frac{3}{4}$ already has the required denominator, nothing needs to be done to $\frac{3}{4}$ .

Since the in $\frac{1}{2}$ needs to be multiplied by in order to get as the deonominator, multiply the numberator of $\frac{1}{2}$ by .

The "new" addition problem is now: $\frac{3}{4}+\frac{2}{4}$ .

The answer to this question is therefore $\frac{5}{4}$ .

Because and do not have a common factor, the answer cannot be simplified.

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Example Question #5 : How To Add Fractions

$\frac{7}{12}+\frac{5}{4}=$

Possible Answers:

$\frac{13}{12}$

$\frac{11}{6}$

$\frac{1}{2}$

$\frac{11}{5}$

$\frac{3}{4}$

Correct answer:

$\frac{11}{6}$

Explanation:

To add two fractions, first find the common denominator. We can convert $\frac{5}{4}$ to $\frac{15}{12}$ . $\frac{7}{12}+\frac{15}{12}= \frac{22}{12}$ , which reduces to $\frac{11}{6}$ .

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Example Question #485 : Arithmetic

Find $\frac{7}{8}+\frac{3}{2}$ .

Possible Answers:

$\large 11$

$\tiny 1$

$\small \frac{8}{19}$

$\tiny {}\frac{19}{8}$

$\large \frac{9}{1}$

Correct answer:

$\tiny {}\frac{19}{8}$

Explanation:

To add two fractions, first find the common denominator, then add the two numerators.

$\frac{7}{8}+\frac{3}{2}=\frac{7}{8} + \frac{12}{8}$

$\frac{7}{8}+\frac{12}{8} = \frac{19}{8}$

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SSAT Middle Level Math : SSAT Middle Level Quantitative (Math)

Study concepts, example questions & explanations for SSAT Middle Level Math

All SSAT Middle Level Math Resources

Example Questions

Example Question #173 : How To Divide Fractions

Example Question #23 : Solve Division Word Problems With Fractions And Whole Numbers: Ccss.Math.Content.5.Nf.B.7c

Example Question #1 : How To Add Fractions

Example Question #224 : Grade 7

Example Question #2 : How To Add Fractions

Example Question #482 : Arithmetic

Example Question #483 : Arithmetic

Example Question #3 : How To Add Fractions

Example Question #5 : How To Add Fractions

Example Question #485 : Arithmetic

All SSAT Middle Level Math Resources

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